1. Field of the Invention
The present invention generally relates to a method for determining the transition zone on a curve between a statistically single exponential function and a composite function of the single exponential and another function. The present invention is particularly useful as it relates to an improved method for accurately determining the thermal neutron decay time constant in a geological formation surrounding a well bore.
2. Description of the Background
Thermal neutron logging of oil and gas wells is an established technique for analysing the subsurface structure and fluid content of geological formations. A downhole instrument containing a pulsed neutron source and two radiation detectors at different spacings from the source is employed in thermal neutron logging techniques. After the logging apparatus is lowered into a borehole, the electrically powered neutron source is activated to provide periodic short bursts of fast neutron radiation. The fast neutrons lose energy and are quickly slowed to thermal velocities by repeated collisions with the nuclei of atoms in the environment, including both the borehole and the surrounding geological formation. However, because the absorption cross section for high energy neutrons is low, most of the emitted high energy neutrons pass through the borehole fluid, casing and cement to interact with the surrounding geological material. Because the cross section for neutron absorption is typically higher for slow or thermal neutrons than for fast neutrons, the low energy, thermal neutrons produced in the surrounding geological formation are more likely to be absorbed.
The absorption of a thermal neutron by a nucleus is often accompanied by subsequent emission of gamma radiation at an energy characteristic of the absorbing element. These reactions are known as neutron-gamma capture reactions. These capture gamma rays may be detected as an indication of the occurrence of the neutron-gamma capture reaction. After the neutron source is turned off, the count rates in the radiation detectors are monitored as a function of time. Detectors directly sensitive to the presence of thermal neutrons may be employed. However, detectors sensitive to the presence of capture gamma radiation, e.g., sodium iodide or cesium iodide scintillation detectors, are more commonly employed.
The low energy, thermal neutrons are particularly likely to participate in nuclear reactions with any of several elements commonly present in the formation. For example, the element chlorine, a common constituent of subterranean waters, has one of the highest cross sections or probabilities for thermal neutron capture with resultant gamma ray emission. Due to the high cross section of chlorine for the capture of thermal neutrons, the rate at which thermal neutrons disappear from the immediate environment of the logging instrument is largely dependent on the concentration of chlorine in the borehole and formation fluids. Because both liquid and gaseous petroleum fluids contain virtually no chlorine, formation petroleum fluids easily may be distinguished from saline fluids by measuring the rate at which capture gamma radiation declines after a neutron source is turned off. As a result of the high cross section of chlorine, the rate of decline is typically much faster in formations bearing saline water than the rate in formations bearing petroleum products.
However, actual borehole decay rates are also dependent on the composition of the surrounding formation and the drilling fluids in addition to the composition of the formation fluids. The rate of radiation time decay is dependent on the total nuclear composition of the environment, of which chlorine comprises only one element. Accordingly, a measurement of the time decay rate provides diagnostic information about the well bore environment in general. The probability of absorption of thermal neutrons in each element is known. Thus, the probability of absorption in each material comprising the environment may be estimated. For example, the probability of absorption in sandstone is different from that of absorption in limestone. Such differences will affect the average time decay measurement. However, with prior knowledge of lithology and porosity, the measured time decay rate may be interpreted to estimate the quantity of water and petroleum in a geological formation. This knowledge is of great importance in the analysis of the economics of petroleum production.
Although the basic time decay measurements may be obtained using only one radiation detector, it has become customary to utilize two separate detectors at different distances from the neutron source, so that the two counting rates may be analyzed and compared. These comparisons permit analysis of the extent of certain errors resulting from the diffusion of neutrons in the formation at the borehole wall. This comparison also permits corrections for the effects of the borehole diameter and for fluid salinity to be calculated and applied. Further, when the detectors are spaced near and far from the neutron source, comparison of the total counting rates yields information about the porosity of the fluid filled pore spaces in the formation.
For a true exponential decay process, the exponential decay law EQU N(t)=N.sub.o exp(-t/.tau.)
states that a measured detector count rate N(t) will be observed at time t following the end of a neutron burst, where N.sub.o is the count rate immediately following the neutron burst and .tau. is the exponential time constant characteristic of the formation. The time constant is related to the total macroscopic thermal neutron capture cross section by the relation EQU .tau.(microseconds)=4550/.SIGMA. (capture units)
where .SIGMA. is the sum of the cross sections of the individual elements in the formation. Experience has established that the exponential decay time constant in typical petroleum formations ranges from approximately 70 microseconds to 1000 microseconds.
Although the theoretical thermal neutron decay curve approximates a perfect exponential, the initial decay observed for actual curves is influenced by effects associated with the well bore. In actual thermal neutron decay curves, the first portion of the decay curve is generally a composite of two or more decay curves. The earliest portion is most influenced by the well bore effects and the later portion more clearly resembles the exponential decay representative of the true neutron decay in the formation. With the passage of sufficient time after each neutron burst, the well bore effects diminish and the thermal neutron decay curve more closely approximates a true, single exponential decay function.
As the population of thermal neutrons continues to decrease exponentially, eventually a point is reached at which the rate of decay of the thermal neutron population is no longer significant compared to background effects. Measurement of the thermal neutron decay time constant must be made during the time between the end of the high energy neutron burst, actually after the initial decay period influenced by the well bore effects has passed, and the time at which the thermal neutron population has decayed to an approximately constant background level. The background counting rate from the detectors must also be determined and subtracted from the measured counting rates to produce a true exponential decay curve corrected for background.
Many methods and devices have been employed to acquire and analyze data representing the radiation time history following a burst of fast neutron radiation in geological formations. Generally, data is acquired in the form of integrated count rates taken during two or more specific intervals following each radiation burst. For example, two fixed time windows have been employed to obtain such data. Exemplary patents disclosing methods and apparatus used in these systems include U.S. Pat. Nos. 3,358,142 issued to Hopkinson and 3,379,884 and 3,379,882 issued to Youmans.
Another approach known as the "normalized sliding gate" technique employs three time gates for data acquisition, wherein the widths and placements of the time gates bear specific relationships to the measured decay constant. This technique is described in U.S. Pat. No. 3,566,116 issued to Nelligan which is incorporated herein by reference for all purposes. In this technique disclosed by Nelligan, the acquisition time gates are positioned so that the background corrected count rate ratio from the first two gates is equal to a predetermined fixed value. The background corrections are obtained from the third gate. The exponential decay constant is deduced from the gate placement required to achieve the desired count rate ratio of the first two gates. The neutron burst repetition rate is adjusted to be more or less frequent as appropriate to the most recent measurement. This technique makes the assumption that the measured time decay function being sampled is a true exponential, which is not always true for measurements made shortly after the neutron burst.
Still another approach involves sampling count rate data in six intervals of fixed but unequal time widths at predetermined and invariant fixed times following the neutron blast. This approach is exemplified in U.S. Pat. Nos. 4,388,529 issued to Peelman 4,409,481 and 4,424,444 issued to Smith. In this approach, the time integrated radiation detection counts from the six windows are processed with a least squares iterative fitting algorithm. The fitting algorithm finds a "best fit" of the measured decay function to a mathematical function consisting of the sum of two separate exponentials and a constant background level. The purpose of the fitting method is to extract not only a slope representative of the formation decay constant, but also, to extract a second time decay slope representing contributions from the decay of the thermal neutron population in the borehole region. In this method, the neutron burst repetition rate and gate placements remain constant and fixed under all measurement conditions.
The most recently disclosed method involves placement of one hundred time analysis acquisition intervals of equal width both during and after the fixed repetition rate neutron burst. This method was disclosed by R. R. Randall in SPE Paper No. 14461 presented in 1985. A single window time averaging time analysis technique is performed on a portion of the data points in order to extract a formation decay constant. The decay function is not tested for exponentiality, but again is assumed to be an exponential decay function in order to make the computation.
The above prior methods for determining the decay constant suffer from several drawbacks. For example, the analysis time gates may not always be optimally placed to produce the best statistics and/or the most accurate measurements. Additionally, the decay function sampled is not always a true exponential, particularly as a result of the borehole effects, and the analysis method may be inappropriate and inaccurate as a result. In these methods, the decay function is not explicitly tested to determine if it may be approximated by an exponential time decay function. Finally, the sum of statistical and systematic errors in the computation may be larger than necessary due either to inadequate sampling intervals which neglect some usable data or to fitting uncertainties which arise when iterative fitting techniques are used.
The present invention overcomes many of the above problems and provides an improved method for accurately determining the thermal neutron decay constant of an unknown material and for testing to ensure that the decay function is a true exponential. An exemplary use of the present invention is to provide an improved method for accurately determining the thermal neutron decay time constant in a geological formation surrounding a well bore.